The Calendar
the Skeptic, Vol 15 No 1
By Roland Seidel
[Note from Web Editor - February 2005: This article appeared in the Skeptic in 1995, and since then several of the links have disappeared. As relocating them was difficult (most could only be found by searching for common words like "calendar"), broken links have been disabled. If anyone knows where they have gone to, please contact us and they will be restored.]
The Calendar
"The calendar is a system designed to reckon time in periods convenient to the conduct of civil life. It is generally based on the natural cycles of moon phases and seasons since the moon has always influenced the timing of religious festivals, and the seasons have set the time of sowing and harvesting and so controlled economic life." [m126]
This is an excellent definition illuminating the dual role of the calendar: religious matters that are arbitrarily timed and agricultural matters that must be precisely timed in the year. It is my opinion that the confusion of these agendas has led to most of the silliness in the calendar. We experience three natural cycles: the day, the month and the year. It is natural to assume that these are related but the illusion of stability that attends them belies the comedy of errors and false hope that is their history. Most of the energy spent in calendric pursuits has gone in the essentially fruitless task of reconciling the cycles of the sun (agriculture) and the moon (religion) using the doubly irreconcilable unit of the day. The following is an incomplete study of the evolution of the calendar that will give you a good idea of the nature of the beast. [p214]
Early agriculturalists began to settle the flood plains of the Tigris-Euphrates valley (modern Iraq just above Kuwait) around 6000 BC. The Sumerians turned up sometime later (3600 BC), coming from an unknown area called Aratta probably near the Caspian Sea, incorporated all the indigenous agricultural terms into their own agglutinative language and came to dominate the area near the Persian Gulf. They invented cuneiform script and were exquisite mathematicians using a number system based on 60 (we use base 10) managing the solution of quadratic, cubic and simultaneous equations. [oe15,37-39][k39-43][f330-340]
Why they chose 60 is not entirely clear; it has lots of factors and they may have been aware that 6 is 'perfect' (factors of 6 add up to 6) but it may also have had something to do with the length of the year which was initially thought to be 360 days comprised of 12 months of 30 days each. (Month = moon of course). They also divided the sky into 12 signs (the astrological ones) and also 360 degrees, each degree having 60 minutes, each minute 60 seconds and each second 60 thirds. They did sums with numbers like 29;55,13,40 (29(55'13"40'") and left us, in that, an ugly legacy. [oe50][i170-181][n21,39][p217]
Meanwhile Semitic peoples who had settled further north were building cities and competing for dominance. Sargon (Akkadian, 2370 BC) took over and later Hammurabi (Babylonian, 1790 BC), subjugating and assimilating the Sumerians. They adopted Sumerian 'science' and retained their language for ritual occasions the way Latin was retained in Europe. Months now alternated 29 and 30 days making a year of 354 days requiring an extra intercalated month now and again to get the seasons to line up properly. There was a lot of astronomical data-gathering on stars and 'bibbu' (meaning sheep - the Greeks later called them 'planetoi' meaning wanderers) and eclipses. [oe16,17][k60,288-290][n21][p217][f343-346]
To see what they were up against we need to pause for some technical terms.
The month is not a simple thing at all. First there is the Synodic month (synod = meeting, in astronomy it means conjunction or lining-up) being the time between successive new moons (29.53059 days mean value, min 29.26, max 29.80). This is a handy size chunk of time that should be useful in measuring the course of the year but it isn't. The Babylonians tried 8 years = 99 months = 2922 days, then 27 years = 334 months but the best approximation was 19 years = 235 months = 6940 days. This last is attributed to Meton (432 BC Athenian Greek) but may have been Babylonian and is preserved today in the Jewish 'Metonic Cycle'. Each of these was used to create a sequence of years where roughly every third year has thirteen months. [oe5,31,55,56][n37,65][p218]
Eclipses present manifold problems that the Babylonians chipped away at with observation; we can approach them from theory. The Moon's orbit is inclined at 5( to the Earth's so eclipses can only occur when the moon crosses the 'ecliptic' (apparent path of the Sun). Such points are called nodes, either ascending or descending. The Draconic month is the time between two ascending nodes (27.21222 days mean value) and since eclipses can only occur when the moon is also full or new we need some nice round numbers where the draconic and synodic month match up. A nice one is 6 synodic months for 61/2 draconic months but it tends to slip fairly quickly being useful for only seven or eight cycles. [oe31]
A further problem is that the moon's orbit is elliptical and it will be travelling faster when closer to earth (nearest = perigee) and slower when further away (furthest = apogee). The Anomalistic month is the time between perigees (27.55455 days mean value). The Babylonians discovered that 223 synodic = 242 draconic = 239 anomalistic = 6585 days (accurate to a few hours) making eclipses fairly predictable. This is also only a couple of weeks more than 18 years. Halley mistakenly thought they referred to it as the Saros Cycle but the name has stuck. [oe29,32,33,69][n35]
Just for completeness there is one more month: the Sidereal month (sidereal = of the stars) when the moon returns to the same position relative to the background stars (27.32166 days mean value). [oe5]
By the sixth century BC the Greeks had taken over everything and refined the convergences. Kallipos (370 BC) took four Metonic cycles and dropped one day to make 76 years = 940 months = 27759 days. Hipparchos did the same to Kallipos and got 304 years = 3760 months = 111035 days but the numbers were getting a bit too silly to be useful by then. [oe56,69][n65]
Euktemon (5th century BC) noted that the times between solstices (longest, shortest days) and equinoxes (equal day and night) were different. The seasons vary from 89 to 94 days due to another orbital irregularity. Time for some more technical terms. [oe56]
The common year is called the Tropical year meaning the time between spring equinoxes (365.24219 days mean value decreasing by 0.000 006 14 days per century). Because the Earth's orbit is elliptical it will travel faster at perihelion (closest, now early January) and slower at aphelion (furthest, now early July). This means that the season around perihelion will be shorter than the one around aphelion. Currently the gaps between equinoxes and solstices are, starting at the Northern Hemisphere Spring Equinox, 92.72, 93.66, 89.84, and 88.98 days. The southern hemisphere gets a few extra days of winter and the northern hemisphere gets a few extra days of summer. [oe4,56,202]
The Anomalistic year is the time between perihelions (365.25964 days mean value). Because it is longer than the tropical the date of perihelion will creep a little later each year - about a month in 200 years - so the hemispheres get to exchange the advantageous seasons eventually. [oe56,57]
The Sidereal year is the time for the Earth to return to the same position relative to the fixed stars (365.25636 days mean value increasing by 0.000 000 12 days per century). Because it is slightly longer than the tropical the equinoxes will gradually creep westward around the ecliptic by 1( in 71.71 years or 360( in 25800 years. This is the famous 'Precession of the Equinoxes' discovered by Hipparchos that so embarrasses astrology. [oe70,80,96,172][n37,39]
Rome conquered Greece in 146 BC and had been developing their own calendar. All of our calendar names come from the Romans including the word calendar itself. The Roman month began when an official went into the streets and shouted out that a new moon had just happened (Ind o-European root kel( = shout, calends = start of month) and announce the ides (13th or 15th day) and the nones (9 days before ides). [m126][e][p219]
Originally there were ten months making a year of 304 days: Martius (Mars, god of war), Aprilus (aperire = to open - buds of spring), Maius (Maia, goddess of fertility), Junius (Juno, goddess of the moon), Quintilis, Sextilis, September, October, November, December - the last being the Roman numbers five to ten. In the 8th century BC King Numa Pompilius added January (Janus, god of doorways) and February (februa, festival of purification) although the year still began on March 1 until 153 BC when it was set to 1 January making the numbered months look silly. [rd390][e]
They still had to have an extra month now and again to fix up the seasons. These 'full years' became somewhat controversial since the start of the year was also the start of public office and the priests who decided which years were to be full tended to favour their friends. By Julius Caesar's time the seasons were a couple of months off and he was not happy. He found the solution when he went to Egypt. [m126,129][e]
Caesar met not only Cleopatra in Egypt but also an astronomer called Sosigenes who explained the Egyptian calendar. The Egyptians had been developing their own system since about 3000 BC and started off with a lunar one just like everybody else but ran into problems very quickly. Egypt is unique in early civilisations in being so dependent on one event: the flooding of the Nile. The moon consistently failed to predict this but the stars were very serviceable. They soon noticed that the heliacal rising of Sirius (first day visible just before sunrise) always preceded the flood by a few days. [m126][oe10][n12][p219]
They eventually had a system of 36 stars to mark out the year and in the end had three different calendars working concurrently for over 2000 years: a stellar calendar for agriculture, a solar year of 365 days (12 months x 30 + 5 extra) and a quasi-lunar calendar for festivals. Sosigenes' message to Caesar was that the moon was a nice god but knew nothing about when things happen. [oe10][n13]
Armed with this information Caesar returned to Rome and made big changes. The old lunar system with intercalary months was abandoned and a new solar system was introduced with fixed month lengths making 365 days and an intercalary day every forth year in February which now had 29 or 30 days. To shift the equinox back to March 25 he added three extra months to 46 BC making it 445 days long ('the year of confusion') and the Julian calendar began on 1 January 45 BC. He also added to the Regnal numbering system (year of king: eg 12th year of the reign of Pompilius) an absolute numbering system setting the beginning at the foundation of Rome (753 BC = 1 AUC, ab urbe condita). They renamed Quintilius Julius in honour of him. [m126][rd390][e][b1][p220,221]
His nephew Augustus (originally named Octavius) also did some cleaning up that is not clear. One source (Britannica) suggests that the priests got the leap years wrong having one every third year for forty years so he had to skip a few until 8 BC. He was the first Emperor anyway so they renamed Sextilis August in his honour but had to pinch a day from February to make it the same length as July. [m126][e]
Things went swimmingly for a while; the seasons were finally staying put in the year and festivals were happening at sensible times - almost. At the Council of Nicea in 1079 AUC (325 AD) Easter was decreed to be the first Sunday after the full moon after the vernal equinox. The early Christians were keen to cleanse pagan ideas (like the spherical Earth) so in 1280 AUC (526 AD) the Abbot of Rome, Dionysius Exiguus proclaimed that the birth of Christ should be the event from which years are counted, calculated that this was December 25 (a handy pagan festival for mid-winter) 753 AUC (at least four years too late - Herod's rule was from 11 BC to 4 BC). He asserted that 754 AUC should now be called 1 AD (anno Domini = in the year of our Lord) and 753 AUC should be called 1 BC (now meaning Before Christ) with prior years counted backwards. The omission of a year zero was a dumb idea. [oe101,103][e][p210,221]
About this time the seven day week was introduced as well although it may have appeared earlier in the Jewish calendar that was tidied up in the fourth century. Cycles of from four to ten days had previously been used for organising work and play. Seven was chosen apparently in acknowledgment of the Genesis story where God rested on the seventh day although there is a strong suggestion that it reflected the seven pagan gods visible in the sky as the planets, sun and moon. The names of the days in Latin countries are sensibly the Roman gods but the English ones are mostly the equivalent Nordic gods. [rd390][p220]
Sunday (sun) = Dimanche (dies Domini, Lord's day)
Monday (moon) = Lundi (moon)
Tuesday (Tiw) = Mardi (Mars, god of war)
Wednesday (Woden, Odin) = Mercredi (Mercury, messenger god)
Thursday (Thor) = Jeudi (Jove, Jupiter, top god)
Friday (Frigg, Freya) = Vendredi (Venus, god of love)
Saturday (Saturn, Roman god of agriculture) = Samedi (Sabbath day)
By the middle ages the seasons had slipped again. Pope Leo X tackled the problem in 1514 by engaging a number of astronomers, among them one Copernicus who quickly recognised that there was a more fundamental problem than rearranging the calendar and rearranged the universe instead by putting the sun at the centre. Work stopped. Half a century later Pope Gregory XIII was game enough to have another go and assembled a team of experts led by the German mathematician Christoph Clavius who spent ten years finding a solution. The church spent another six years working out how to implement it receiving final approval in 1582. [e][p223]
The change was this: skip ten days sometime to bring the seasons back in line and skip a few leap years now and again. The extra day every fourth year is too much so skip the leap year at the end of the century. This is now a touch short so put back a leap year every fourth century.
Simple isn't it? The rule is: a year is leap if it is a multiple of 4, it is not leap if it is a multiple of 100, it is back to being leap if it is a multiple of 400. Since this still produces an error of a day in 3,323 years we will also skip the leap year in 4000 AD. So in 1582, October 4 was followed by October 15, 1600 was a leap year but 1700, 1800 and 1900 were not. 2000 will be a leap year. [m126][e][b1][p223,224]
The changeover was not smooth. France, Spain, Italy, and Portugal changed in 1582; Prussia, Switzerland, Holland, Flanders and the German Catholic states in 1583; Poland in 1586 and Hungary in 1587. The Protestant countries weren't too keen to follow so for nearly two centuries there were two calendars running in Europe ten days apart. England had just shifted the start of the year from December 25 to March 25 a couple of centuries ago and they weren't about to jump on any new Catholic bandwagon. George Washington's birthday could be equally stated as February 22 1732 NS (new style) or February 11 1731 OS (old style) and letters usually carried both dates. [e][b1][p224]
Matters came to a head in 1700 when the Protestants had a leap year and the Catholics didn't, increasing the gap to 11 days. Denmark and the German Protestant states changed in 1700 and Sweden came up with the brilliant plan of simply skipping all leap years until they caught up in 1740. England and America switched over in 1752, skipping 11 days by making September 3 September 14 and shifting the start of the year to January 1. There was much unrest - 'give us back our eleven days' was a popular campaign slogan. [b1][n238][e][p224]
Many other countries were slow to adopt the standard and it was not until early this century that the entire world was finally synchronised. Japan changed in 1872, China in 1912, Bulgaria in 1915, Turkey in 1917, Yugoslavia and Rumania in 1919 and Greece in 1923. Russia made the switch after the October revolution which actually happened in November (25 October OS = 7 November NS). The Gregorian calendar is now recognised world wide although there are still many other calendars running alongside it for religious purposes. [e][b1]
The Metonic cycle of 19 years has twelve years of 12 months and seven years of 13 months, generally alternating 29 and 30 days. In the fourth century the Jews refined this to suit their festival requirements. The 3rd, 6th, 8th, 11th, 14th, 17th and 19th years of each cycle have 13 months (384 days) and the others 12 months (354 days) . The day begins at sunset (6 p.m.) and the week has seven days only the last of which is named (Sabbath). The years are numbered from the Jewish creation of the world (3761 BC) and are occasionally lengthened or shortened to meet certain rules. [b3][m129][rd392][p222]
The extra months ensure that Passover is celebrated in the month of Abib (fresh ears of grain). The Day of Atonement (10 Tishri, Yom Kippur) must not fall on the 1st or 6th day and the seventh day of Tabernacles must not fall on the Sabbath. The New Year festival (1 Tishri, Rosh Hashanah) must be celebrated on the day the moon becomes visible. This means that the eighth month, Cheshvan, sometimes has 30 days instead of 29 (a 'redundant' year) and the ninth month, Kislev, sometimes has 29 instead of 30 (a 'defective' year). Jewish years are described by a three letter 'characteristic' indicating respectively the day of the week for New Year, the type (regular, redundant or defective), and the day of the week for Passover. This is followed by the word for 'leap' or 'ordinary'. There are 14 possible Jewish years. The year 5755 began on September 6 1994. [b3]
This is the only truly lunar calendar left, very similar to the old Babylonian Calendar, having 12 months alternating 29 and 30 days making 354 days altogether. Occasionally an extra day is included in the last month to ensure the year begins with the new moon. It has no connection with the sun and seasons and while 32 Christian years go by, the Muslims enjoy nearly 33. Years are counted from Mohammed's flight from Mecca (the Hegira) on 16 July 622 AD. The year 1415 began in early June 1994. [m128][rd392][p222]
There are a couple of Ecclesiastical calendars for organising festivals, a Chinese calendar banned in China but used in some Asian countries, in remote areas like the Russian steppe there are still remnants of simple agricultural calendars which depend on equinoxes but not on counting days and dozens of provincial calendars. [b9-19][r1-185]
The French Revolution against the aristocracy and the church insisted on radical change with immediate impact. The church ran the calendar so it had to go. They adopted the old Egyptian one with 12 months of 30 days being 3 decades, the last day of each decade was a day of rest. Five spare days (Sansculottides) were for pleasure and feasting. The Republican Era began on 22 September 1792 (Year I) and ended on 31 December 1805 after it became clear that the rest of the world was having difficulty with it. Leap days happened in September and the year VIII was leap where the corresponding Gregorian 1800 was not. [b20][r62]
Auguste Compte, the founder of Positivism, offered a plan in April 1849 for a calendar. It has 13 months of 28 days each, always 4 weeks, always starting on Sunday. The spare day called 'Year End Day' followed December and was not in the weekly round. The sequence Saturday December 28, Year End Day, Sunday January 1 ensured identical months. The extra month, Sol, after June was followed by 'Leap Year Day' as appropriate. He used the names of eminent men for each month, week and day and event (559 in all) consecrating Leap Year Day to 'Eminent Women'. France tried it for a while in 1849 and it gained much support in the US. [w258-266][r62-63]
The minimum impact suggestion is to divide the year evenly into four identical quarters each having months of 31, 30 and 30 days and exactly 13 weeks. Use the Year Day and Leap Day as before to ensure that every quarter begins on Sunday. This repairs the unevenness of the quarter and half year and much of the irregularity of the months while fiddling with only 8 days in a normal year and 4 in a leap. It really is the only prospect for modern reform. [w267-273]
In October 1931 The International Calendar Association put before the League of Nations a plan for modern calendar reform. They listed the problems of the Gregorian as: it was designed for an agricultural world 2000 years ago, it still tries to match lunar and solar agendas (Easter), it begins at a silly time, the seven day week is too long, random month length, complicated leap years, irregular national holidays, stupid base 60 sums. Their suggestion was for the 365 day year to be divided into 5 quintals of 73 days each. A quintal has 12 six-day weeks, the last day of the week and of the quintal being rest days making 300 work and 65 rest days in the year. The day has 12 hours, the hour 100 minutes and the minute 100 seconds. Leap years occur every fourth year unless it is a multiple of 128 (accurate to 90 minutes in 1,000,000 years). It is still before the UN. [r186-194]
Finally, when does the 21st century begin? Because we have no zero year the first century comprised years 1 to 100, the second years 101 to 200, the third years 201 to 300 and so on. Clearly 2000 AD is the last year of the 20th century and 2001 is the first of the 21st. The millennium technically begins on 1 January 2001. This won't deter people from feeling that 1 January 2000 is the changeover just as they did in the Middle Ages for 1000 AD. Never let facts stand in the way of a good story. [p222]
Coyne: This is subtitled Proceedings of the Vatican Conference to Commemorate its 400th Anniversary 1582-1982. It includes a copy of the 1582 Papal Bull. Richmond: A compendium of just about every calendar ever thought of including the submission of the World Calendar Committee to the League of Nations in 1931. Richmond was the organiser and secretary of the committee. O'Neil: Both books are exquisitely detailed - more figures than you can poke a stick at. North: The authority on astronomic and astrologic history. The Fontana series are superb.
[b] Butler, Audrey (1987) Dictionary of Dates. London, Dent.
[c] Coyne, G.V. et al(1982). Gregorian Reform of the Calendar. Vatican, Pontificia Academia Scientiarvm.
[e] Encyclopaedia Britannica (1965).
[f] Fagan, Brian M. (1986). People of the Earth. Boston, Little, Brown and Company.
[i] Ifrah, George (1987) From One to Zero. A Universal History of Numbers. New York, Penguin.
[k] Kramer, Samual Noah (1963) The Sumerians. Their History, Culture and Character. Chicago, University of Chicago Press.
[m] The Macquarie History of Ideas. (1983) Sydney, Macquarie Library.
[n] North, John (1994) The Fontana History of Astronomy and Cosmology. London, Fontana Press.
[ot] O'Neil, W. M. (1975) Time and the Calendar. Sydney, Sydney University Press.
[oe] O'Neil, W. M. (1986) Early Astronomy. Sydney, Sydney University Press.
[p] Paul, Richard (1993) A Handbook to the Universe. Chicago, Chicago Review Press.
[rd] The Reader's Digest Book of Facts (1986) Sydney, Reader's Digest.
[r] Richmond, B. (1956) Time Measurement and Calendar Construction. Leiden, E. J. Brill
[w] Wilson, P. W. (1937) The Romance of the Calendar. London, Allen and Unwin.
Thanks to the people below who have added further information on the Calendar
Length of the Year is wrong.
"The common year is called the Tropical year meaning the time between spring equinoxes (365.24219 days mean value decreasing by 0.000 006 14 days per century)."
This is false! The mean interval between vernal equinoxes is currently 365.24238 days (real Universal Calendar days) and will increase to a local maximum over the next millenia (slowly and in fits and starts) to somewhere close to or above 365.242424 days. The year length that is currently 365.24219 days (and decreasing) is the average tropical year (averaged over the whole tropical zodiac), or equivalently the time it takes the MEAN tropical longitude of the sun to increase by 360 degrees, and therefore has nothing more to do with the vernal equinox than it has to do with the fall equinox, the solstices or any other point of the tropical zodiac!
See my web pages at: http://www.magnet.ch/serendipity/hermetic/cal_stud/cassidy/index.html for some examples of the consequences of the promulgation of this mistake.
Yours sincerely Simon Cassidy
More detail on the Swedish changeover.
To make the change from the Julian calendar to the Gregorian, it is true that Sweden decided to skip the leap years from 1700 to 1740 to make the change smooth, just as Seidel writes. But he does not write that Sweden did not fulfil the plan. They skipped the leap year only in 1700.
1704 and 1708 became leap years again, making Sweden out of phase with the rest of the world.
The Swedes did not like being one day drifted from their neighbours. So they decided to return to the Julian calendar in 1712 by making it a double leap year, February having 30 days. It was not until 1753 that Sweden eventually adopted the Gregorian calendar, by letting February 17th be followed by March 1st.
One of my hobbies is genealogy. The details about the Swedish calendar are well-known facts among Swedish genealogists. They are e.g. obvious from the church records, which are the single most valuable sources for Swedish genealogy. One of my remote relatives was born on Feb 30th 1712.
A site which might be of some interest for you is http://www.genealogi.se/tid.htm
Among the links at the web site, there is also a link to an Australian genealogy society: "Canberra Dead Persons Society": http://www.pcug.org.au/~mpahlow/welcome.html
Torbjorn Gustavsson
The Positivist Calendar
The statement on The Positivist Calendar confuses Auguste Comte’s calendar with a calendar plan promoted 50 years later by Moses Cotsworth.
Find out more about each calendar reform plan by visiting the Home Page for Calendar Reform. http://personal.ecu.edu/mccartyr/calendar-reform.html I recommend starting with the new, interactive Positivist Calendar at:
http://personal.ecu.edu/mccartyr/pos-cal.html
Rick McCarty
Other interesting links
- Calendar land. Includes celestial, cultural, and interactive calendars:
- http://www.calendarzone.com
- Calendar Conversions from any calendar into any other:
- http://genealogy.org/~scottlee/calconvert.cgi
- Calendars and their History:
- http://astro.nmsu.edu/~lhuber/leaphist.html
- Doomsday Algorithm for Day of Week:
- http://rudy.ca/doomsday.html
- The Human Calendar
- http://www.simpleage.com
- The Calendar FAQ:
- http://www.pip.dknet.dk/~pip10160/calendar.html *
* ...just type Calendar in a browser. There’s lots of them: Aztec, Roman, Hebrew, Iranian, Goddess, Native American, Javanese...
Scott Flansburg (a.k.a. "The Human Calculator", Guinness Book of Records 2000) has introduced the Human Calendar which is mathematically sound and based on the 28 day cycle. http://www.simpleage.com
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